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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

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Topological constraints on real algebraic surfaces from mean curvature constraints

The mean curvature of a real algebraic surface $S$ in $\mathbb{R}^3$ defined as the zeroes of a polynomial $P$ of degree $d$ with real coefficients in three variables is given by the formula \begin{eq …